Bij FinSet prop functor

• The inclusion \(\mathbf{Bij} \overset{i}{\hookrightarrow} \mathbf{FinSet}\) is a prop functor.

• There is a prop functor \(\mathbf{Bij} \xrightarrow F \mathbf{Rel_{Fin}}\) defined by \(F(\bar{m} \xrightarrow{f} \bar{n}):=\{(i,j)\ |\ f(i)=j\} \in \bar m \times \bar n\)